🤖 AI Summary
This work addresses the issue of severe reward inequality among agents in multi-agent delegation settings, which often arises when traditional contract mechanisms prioritize the principal’s utility maximization. To mitigate this, the paper introduces the notion of “non-discriminatory pricing” and incorporates fairness constraints into contract design, thereby formally characterizing the trade-off between utility loss and fairness. Leveraging tools from mechanism design, game theory, and optimization—combined with approximation analysis and constraint relaxation techniques—the study establishes a tight upper bound of \(O(\log n)\) on non-discriminatory prices, where \(n\) denotes the number of agents. Moreover, it demonstrates that allowing minimal discrimination reduces this bound to a constant. This work thus provides the first complete quantitative characterization of the fairness–efficiency trade-off curve in multi-agent contracts.
📝 Abstract
We study multi-agent contracts, in which a principal delegates a task to multiple agents and incentivizes them to exert effort. Prior research has mostly focused on maximizing the principal's utility, often resulting in highly disparate payments among agents. Such disparities among agents may be undesirable in practice, for example, in standardized public contracting or worker cooperatives where fairness concerns are essential. Motivated by these considerations, our objective is to quantify the tradeoff between maximizing the principal's utility and equalizing payments among agents, which we call the price of non-discrimination. Our first result is an almost tight bound on the price of non-discrimination, which scales logarithmically with the number of agents. This bound can be improved to a constant by allowing some relaxation of the non-discrimination requirement. We then provide a comprehensive characterization of the tradeoff between the level of non-discrimination and the loss in the optimal utility.